Question

How do the “span” and “basis” of a subspace differ?

Answer 1

Question 1. How do the “span” and “basis” of a subspace differ?

Solution. The term “span of subspace” is not used. There is a notion of “span of a subset”. It is the subspace of all linear combinations of elements of the set. Now we see that the span of a subspace $V$ is the same subspace $V$, that is why it is not interested to consider the span of a subspace.

At the same time a basis of the subspace $V$ is a linearly independent subset of $V$ which spans $V$. It is strictly less than $V$, at least because it cannot contain zero.

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